(-4s^2+8s+8)-(8s^2+12s-4)=0

Solution for (-4s^2+8s+8)-(8s^2+12s-4)=0 equation:

Simplifying
(-4s2 + 8s + 8) + -1(8s2 + 12s + -4) = 0

Reorder the terms:
(8 + 8s + -4s2) + -1(8s2 + 12s + -4) = 0

Remove parenthesis around (8 + 8s + -4s2)
8 + 8s + -4s2 + -1(8s2 + 12s + -4) = 0

Reorder the terms:
8 + 8s + -4s2 + -1(-4 + 12s + 8s2) = 0
8 + 8s + -4s2 + (-4 * -1 + 12s * -1 + 8s2 * -1) = 0
8 + 8s + -4s2 + (4 + -12s + -8s2) = 0

Reorder the terms:
8 + 4 + 8s + -12s + -4s2 + -8s2 = 0

Combine like terms: 8 + 4 = 12
12 + 8s + -12s + -4s2 + -8s2 = 0

Combine like terms: 8s + -12s = -4s
12 + -4s + -4s2 + -8s2 = 0

Combine like terms: -4s2 + -8s2 = -12s2
12 + -4s + -12s2 = 0

Solving
12 + -4s + -12s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -1s + -3s2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -1s + -3s2)' equal to zero and attempt to solve:

Simplifying
3 + -1s + -3s2 = 0

Solving
3 + -1s + -3s2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1 + 0.3333333333s + s2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.3333333333s + 1 + s2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.3333333333s + s2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.3333333333s + s2 = 0 + 1
0.3333333333s + s2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.3333333333s + s2 = 1

The s term is 0.3333333333s.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333s + 0.02777777779 + s2 = 1 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333s + s2 = 1 + 0.02777777779

Combine like terms: 1 + 0.02777777779 = 1.02777777779
0.02777777779 + 0.3333333333s + s2 = 1.02777777779

Factor a perfect square on the left side:
(s + 0.1666666667)(s + 0.1666666667) = 1.02777777779

Calculate the square root of the right side: 1.013793755

Break this problem into two subproblems by setting 
(s + 0.1666666667) equal to 1.013793755 and -1.013793755.

Subproblem 1
s + 0.1666666667 = 1.013793755

Simplifying
s + 0.1666666667 = 1.013793755

Reorder the terms:
0.1666666667 + s = 1.013793755

Solving
0.1666666667 + s = 1.013793755

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + s = 1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + s = 1.013793755 + -0.1666666667
s = 1.013793755 + -0.1666666667

Combine like terms: 1.013793755 + -0.1666666667 = 0.8471270883
s = 0.8471270883

Simplifying
s = 0.8471270883

Subproblem 2
s + 0.1666666667 = -1.013793755

Simplifying
s + 0.1666666667 = -1.013793755

Reorder the terms:
0.1666666667 + s = -1.013793755

Solving
0.1666666667 + s = -1.013793755

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.1666666667 + s = -1.013793755 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + s = -1.013793755 + -0.1666666667
s = -1.013793755 + -0.1666666667

Combine like terms: -1.013793755 + -0.1666666667 = -1.1804604217
s = -1.1804604217

Simplifying
s = -1.1804604217

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.8471270883, -1.1804604217}
Solution
s = {0.8471270883, -1.1804604217}